Finite Group Databasebeta

← #24997059

Subgroups — #24997059

Order 11008.

692 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145343C211yesmaximal, characteristic
2C2×#14583212C211yesmaximal, characteristic, complemented
3#19135431C211yesmaximal, characteristic, complemented
4#19134681C211yesmaximal, characteristic, complemented
5#19133163C211yesmaximal, characteristic, complemented
6#19132443C211yesmaximal, characteristic, complemented
7C43×#2501C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9#14583212—22no—
10#14583212—22no—
11#14583212—21no—
12#14583210—21no—
13#14583133—22no—
14#14583033—21no—
15#14583032—21no—
16C2×#13063258—21no—
17C2×#13063245—21no—
18C2×#13063239—22no—
19C2×C22⋊(C43⋊C8)C2211yescharacteristic
20C2×C22⋊(C43⋊C8)C2211yescharacteristic
21#14582759C2211yescharacteristic
22#14582661—22no—
23#14582633—22no—
24C2×#123×C43—22no—
25C2×#121×C43C2211yescharacteristic
26C22×C4⋊C4×C43C2211yescharacteristic
27C43×#399—22no—
28C43×#390—21no—
29C43×#384—21no—
30C4×C22⋊C4×C43C2211yescharacteristic
31C22×D172D411yescharacteristic
32C22×C22⋊D43—21no—
33C2×#10621882—22no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8D412yes—
36#13063299—21no—
37#13063299—21no—
38#13063299—21no—
39#13063299—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43D411yescharacteristic
42C2×C22⋊Dic43—21no—
43C2×(C2×D43)⋊C4—21no—
44#13063258—22no—
45#13063258—24no—
46#13063246—22no—
47#13063245—22no—
48#13063245—24no—
49#13063239—44no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)D412yes—
54C43⋊#95—21no—
55C22×D4×C43—21no—
56C22×D4×C43D411yescharacteristic
57C23×C4×C43—21no—
58C23×C4×C43C2311yescharacteristic
59#123×C43—44no—
60#123×C43—44no—
61#121×C43—21no—
62#121×C43—21no—
63#121×C43—21no—
64#121×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43—24no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43D412yes—
72C2×C4⋊C4×C43D411yescharacteristic
73C2×C22⋊C4×C43—24no—
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43D412yes—
76C2×C42×C43—21no—
77#95×C43—21no—
78C24×C43—21no—
79C24×C43C2×D411yescharacteristic
80C23×D43—21no—
81C2×D4×C43—21no—
82C2×D4×C43—21no—
83C2×D4×C43—42no—
84C2×D4×C43—41no—
85C2×D4×C43—41no—
86C2×D4×C43—42no—
87C2×D4×C43—42no—
88C22×C4×C43—22no—
89C22×C4×C43—22no—
90C22×C4×C43—21no—
91C22×C4×C43—42no—
92C22×C4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43—42no—
95C22×C4×C43—42no—
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43#4111yescharacteristic
102C2×C22⋊D43—41no—
103C2×C22⋊D43—41no—
104C2×C22⋊D43—42no—
105C2×C22⋊D43—42no—
106C22×Dic43—21no—
107C22×Dic43—41no—
108C2×D172—21no—
109C2×D172—21no—
110C2×D172—42no—
111C4⋊C4×C43—22no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—22no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—48no—
116C4⋊C4×C43—41no—
117C4⋊C4×C43—41no—
118C22⋊C4×C43—22no—
119C22⋊C4×C43—48no—
120C22⋊C4×C43—41no—
121C22⋊C4×C43—41no—
122C22⋊C4×C43D814yescomplemented
123C42×C43—42no—
124C22⋊Dic43—42no—
125#10621882—82no—
126(C2×D43)⋊C4—41no—
127(C2×D43)⋊C4—41no—
128C4⋊Dic43—21no—
129C4⋊Dic43—21no—
130C4⋊Dic43—42no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8—22no—
133C2×C43⋊C8—42no—
134C2×C43⋊C8—42no—
135C23×C43—41no—
136C23×C43—41no—
137C23×C43—42no—
138C23×C43—42no—
139C23×C43—41no—
140C23×C43—42no—
141C23×C43#12011yescharacteristic
142C23×C43#12111yescharacteristic
143C23×C43#12711yescharacteristic
144C23×C43C2×D812yes—
145C23×C43AGL(1,ℤ/8)12yes—
146C22×D43—41no—
147C22×D43—42no—
148C22×D43—81no—
149C22×D43—81no—
150D4×C43—42no—
151D4×C43—81no—
152D4×C43—82no—
153D4×C43—81no—
154D4×C43—81no—
155C2×C4×C43—22no—
156C2×C4×C43—22no—
157C2×C4×C43—22no—
158C2×C4×C43—24no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—42no—
163C2×C4×C43—42no—
164C2×C4×C43—41no—
165C2×C4×C43—42no—
166C2×C4×C43—44no—
167C2×C4×C43—42no—
168C2×C4×C43—82no—
169C2×C4×C43—81no—
170C2×C4×C43—81no—
171C2×C4×C43#12011yescharacteristic
172C2×C4×C43#12011yescharacteristic
173C2×C4×C43#12111yescharacteristic
174C2×C4×C43#12111yescharacteristic
175C22⋊D43—82no—
176C22⋊D43—81no—
177C22⋊D43—81no—
178C2×Dic43—41no—
179C2×Dic43—42no—
180C2×Dic43—81no—
181C2×Dic43—81no—
182C2×Dic43—81no—
183D172—42no—
184D172—42no—
185C43⋊C8—42no—
186C43⋊C8—42no—
187#9952—431nomaximal, Sylow
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—42no—
195C22×C43—42no—
196C22×C43—84no—
197C22×C43—81no—
198C22×C43—81no—
199C22×C43—81no—
200C22×C43#39211yescharacteristic
201C22×C43#44712yes—
202C22×C43#45912yes—
203C22×C43#49311yescharacteristic
204C22×C43#49611yescharacteristic
205C2×D43—81no—
206C2×D43—81no—
207C2×D43—81no—
208C2×D43—162no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—44no—
213C4×C43—82no—
214C4×C43—81no—
215C4×C43#45812yes—
216Dic43—81no—
217Dic43—161no—
218#3186—431no—
219C2×#480—431no—
220#2501D4311yescharacteristic, complemented
221#1964—431no—
222#1823—431no—
223#1519—431no—
224#1282—431no—
225C2×C43—21no—
226C2×C43—22no—
227C2×C43—22no—
228C2×C43—21no—
229C2×C43—161no—
230C2×C43#200911yescharacteristic
231C2×C43#201111yescharacteristic
232C2×C43#202211yescharacteristic
233D43—161no—
234C2×#123—22no—
235C2×#121—431no—
236C2×#121C2×D4311yescharacteristic
237C22×C4⋊C4C2×D4311yescharacteristic
238#480—862no—
239#480—861no—
240#480—862no—
241#480—861no—
242#466—862no—
243#447—861no—
244#447—861no—
245C2×#107—861no—
246C2×#102—861no—
247C2×#99—862no—
248C2×C22⋊C8—431no—
249C2×C22⋊C8—431no—
250#399—22no—
251#390—21no—
252#384—21no—
253#380—431no—
254C4×C22⋊C4C2×D4311yescharacteristic
255#340—862no—
256#327—862no—
257C43#995211yescharacteristic, complemented, Sylow
258C22×D4—21no—
259C22×D4—431no—
260C22×D4—861no—
261C22×D4C22⋊D4311yescharacteristic
262C23×C4—21no—
263C23×C4C22×D4311yescharacteristic
264C2×D8—862no—
265C22×C8—432no—
266C22×C8—861no—
267#123—44no—
268#123—44no—
269#121—21no—
270#121—21no—
271#121—21no—
272#121—21no—
273#121—861no—
274#121—861no—
275#121—861no—
276#121—861no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—431no—
284C2×C4⋊C4—861no—
285C2×C4⋊C4C22⋊D4312yes—
286C2×C4⋊C4C22⋊D4311yescharacteristic
287C2×C22⋊C4—24no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—861no—
290C2×C22⋊C4—861no—
291C2×C22⋊C4C22⋊D4312yes—
292C2×C42—21no—
293#107—864no—
294#107—862no—
295#102—864no—
296#102—862no—
297#102—862no—
298#99—1724no—
299C22⋊C8—432no—
300C22⋊C8—861no—
301C22⋊C8—861no—
302C22⋊C8—861no—
303#95—21no—
304#95—861no—
305C24—21no—
306C24—861no—
307C24C2×C22⋊D4311yescharacteristic
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—42no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—42no—
314C2×D4—42no—
315C2×D4—861no—
316C2×D4—861no—
317C2×D4—1722no—
318C2×D4—1721no—
319C2×D4—1721no—
320C2×D4—1722no—
321C2×D4—1722no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—21no—
325C22×C4—42no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—861no—
331C22×C4—1721no—
332C22×C4D4×D4311yescharacteristic
333C22×C4D4×D4311yescharacteristic
334C22×C4D4×D4311yescharacteristic
335C22×C4#1062190011yescharacteristic
336C22×C4C2×C22⋊D4311yescharacteristic
337C22×C4C2×C22⋊D4311yescharacteristic
338D8—3442no—
339C2×C8—862no—
340C2×C8—862no—
341C2×C8—1722no—
342C2×C8—1722no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—21no—
347C4⋊C4—48no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—861no—
351C4⋊C4—861no—
352C4⋊C4—1722no—
353C22⋊C4—22no—
354C22⋊C4—48no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—1722no—
358C22⋊C4—1721no—
359C22⋊C4—1721no—
360C22⋊C4#1062188214yescomplemented
361C42—42no—
362C23—41no—
363C23—41no—
364C23—42no—
365C23—42no—
366C23—41no—
367C23—42no—
368C23—3441no—
369C23—3441no—
370C23—1721no—
371C23—1722no—
372C23#1306329411yescharacteristic
373C23#1306329611yescharacteristic
374C23#1306332111yescharacteristic
375C23C2×#1062188212yes—
376C23#1306335112yes—
377D4—42no—
378D4—81no—
379D4—82no—
380D4—81no—
381D4—81no—
382D4—3441no—
383D4—3441no—
384D4—3442no—
385D4—1722no—
386D4—1722no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—24no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—44no—
399C2×C4—42no—
400C2×C4—82no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—3441no—
404C2×C4—3441no—
405C2×C4—3441no—
406C2×C4—1721no—
407C2×C4—1722no—
408C2×C4#1306329311yescharacteristic
409C2×C4#1306329311yescharacteristic
410C2×C4#1306329711yescharacteristic
411C2×C4#1306329711yescharacteristic
412C8—1722no—
413C8—1722no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—42no—
421C22—42no—
422C22—84no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—3441no—
427C22—3441no—
428C22—3441no—
429C22—6882no—
430C22#1458280711yescharacteristic
431C22#1458303312yes—
432C22#1458309112yes—
433C22#1458327511yescharacteristic
434C22#1458328611yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—44no—
439C4—82no—
440C4—81no—
441C4—3441no—
442C4—6881no—
443C4#1458308812yes—
444C2—22no—
445C2—21no—
446C2—22no—
447C2—21no—
448C2—161no—
449C2—6881no—
450C2#1913565511yescharacteristic
451C2#1913566611yescharacteristic
452C2#1913572311yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#2501C2
socleC22×C43#392
prime radical#19145343C2
hypercenter#2501D43
hypocenterC43#9952
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2501

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#14583212C2semidirect
3. #19135431C2semidirect
4. #19134681C2semidirect
5. #19133163C2semidirect
6. #19132443C2semidirect
7. C43×#2501C2semidirect
122. C22⋊C4×C43D8semidirect
220. #2501D43semidirect
257. C43#9952semidirect
360. C22⋊C4#10621882semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191453432
C2×#145832122
#191354312
#191346812
#191331632
#191324432
C43×#25012
#995243